A note on Δ₁ induction and Σ₁ collection

• Autorzy: Neil Thapen
• Języki publikacji: EN

Abstrakty

EN

Slaman recently proved that Σₙ collection is provable from Δₙ induction plus exponentiation, partially answering a question of Paris. We give a new version of this proof for the case n = 1, which only requires the following very weak form of exponentiation: "$x^y$ exists for some y sufficiently large that x is smaller than some primitive recursive function of y".

Kategorie tematyczne

• 03F30: First-order arithmetic and fragments
• 03H15: Nonstandard models of arithmetic

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 186
• Numer: 1
• Strony: 79-84

Daty

wydano

2005

Twórcy

autor

Neil Thapen

• St Hilda's College, University of Oxford, Oxford OX1 4DY, UK

Identyfikatory

DOI

10.4064/fm186-1-6